Per my understanding of their method, the participants were just asked to do the survey without mentioning what was being measured. It's like you said, someone can manage their expression of confidence to a degree (or not, maybe), but privately they may not do that, i.e. when just doing some surveys for a study. One thing I remember from running my own studies like this: usually the participant is subjected to a series of such tests (called a battery, sometimes) in succession so they're likely to get fatigued. I think that's a tougher effect that can possibly confound studies. Though I am not sure mental fatigue matters so much for this study.

Edit: I'd share the article but have no idea where to host it.